Question

Find the number of ways of forming a committee of $5$ members out of $6$ Indians and $5$ Americans so that always the Indians will be in majority in the committee

Answer 1

For Indians to be in majority , we can select

$5$ Indians in $6$ ways

$4$ Indians ans $1$ American in $15\times 5=75$ ways

$3$ Indians and $2$ Americans in $20\times 10=200$ ways

Totals number of ways we can form committee is $200+75+6=281$ ways